Viscosity Dependence of the Folding Rates of Proteins

The viscosity (η) dependence of the folding rates for four sequences (the native state of three sequences is a β sheet, while the fourth forms an α helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation, we show that the folding rates increase linearly at low viscosities η, decrease as 1/η at large η, and have a maximum at intermediate values. The Kramers' theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn α-helix topology is about 500 ns, whereas for β sheet it is about 10μs.